Shape of a Slope Function

Below you can see the graph of a quadratic polynomial f(x)=-0.5x^2+2x+4

#1. Try to find out how the coordinates of point M are connected with point P and the slope m of tangent t by dragging point P with the mouse.
#2. Right click (Mac OS: ctrl-click) point M and select "Trace on". When you move point P now you get the graph of the slope function of f(x). What does the shape of the slope function look like?
#3. Click the little icon in the right upper corner to reset the construction. Change the values of the sliders a, b, and c and turn on the trace of point M again. What does the shape of the slope function look like when you move point P now?